462 lines
15 KiB
Java
462 lines
15 KiB
Java
package de.wwwu.awolf.presenter.algorithms.advanced;
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import de.wwwu.awolf.model.Interval;
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import de.wwwu.awolf.model.Line;
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import de.wwwu.awolf.model.Point;
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import de.wwwu.awolf.model.communication.AlgorithmData;
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import de.wwwu.awolf.model.communication.Data;
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import de.wwwu.awolf.model.communication.SubscriberType;
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import de.wwwu.awolf.presenter.Presenter;
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import de.wwwu.awolf.presenter.algorithms.Algorithm;
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import de.wwwu.awolf.presenter.util.IntersectionComputer;
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import de.wwwu.awolf.presenter.util.Logging;
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import java.util.*;
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import java.util.concurrent.Flow;
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/**
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* Implementierung verschiedener Algorithmen zur Berechnung von Ausgleichsgeraden.
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*
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* @Author: Armin Wolf
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* @Email: a_wolf28@uni-muenster.de
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* @Date: 28.05.2017.
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*/
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public class LeastMedianOfSquaresEstimator implements Algorithm, Flow.Publisher<Data> {
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private List<Line> setOfLines;
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private int n;
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private double quantileError;
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private int kPlus;
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private int kMinus;
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private Queue<Interval> intervals;
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private Interval subSlabU1;
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private Interval subSlabU2;
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private Line sigmaMin;
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private double heightsigmaMin;
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private double intersectionsPoint;
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private double constant = 0.5;
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private double slope;
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private double yInterception;
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private Flow.Subscriber<? super AlgorithmData> subscriber;
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/**
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* Konstruktor
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*
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* @param setOfLines Liste der Geraden
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* @param presenter Presenter (Beobachter)
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*/
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public LeastMedianOfSquaresEstimator(List<Line> setOfLines, Presenter presenter) {
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this.setOfLines = setOfLines;
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n = setOfLines.size();
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double qPlus = 0.5;
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quantileError = 0.1;
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double qMinus = qPlus * (1 - quantileError);
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kMinus = (int) Math.ceil(n * qMinus);
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kPlus = (int) Math.ceil(n * qPlus);
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this.subscribe(presenter);
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}
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/**
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* Konstruktor
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*
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* @param setOfLines Liste der Geraden
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*/
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public LeastMedianOfSquaresEstimator(List<Line> setOfLines) {
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this(setOfLines, null);
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}
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/**
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* Algorithmus zum berechnen des LMS-Schätzers
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* <p>
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* Paper:
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* Mount, David M, Nathan S Netanyahu, Kathleen Romanik, Ruth Silverman und Angela Y Wu
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* „A practical approximation algorithm for the LMS line estimator“. 2007
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* Computational statistics & data Analysis 51.5, S. 2461–2486
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*/
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@Override
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public Line call() {
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Logging.logInfo("=== S T A R T - L M S ===");
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long start;
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long end;
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start = System.currentTimeMillis();
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//(2.) Let U <- (-inf, inf) be the initial active intervals...
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Comparator<Interval> comparator = (o1, o2) -> {
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if (o1.getDistance() < o2.getDistance()) {
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return -1;
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}
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if (o1.getDistance() > o2.getDistance()) {
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return 1;
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} else {
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return 0;
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}
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};
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intervals = new PriorityQueue<>(comparator);
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intervals.add(new Interval(-10000, 10000));
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heightsigmaMin = Double.MAX_VALUE;
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//(3.) Apply the following steps as long as the exists active intervals
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boolean active = true;
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Interval interval;
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while (!this.intervals.isEmpty()) {
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interval = this.intervals.peek();
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if (interval.getActivity()) {
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//(a.) Select any active Interval and calc. the inversions
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int numberOfIntersections = countInversions(interval);
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//(b.) apply plane sweep
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if ((constant * n) >= numberOfIntersections) {
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sigmaMin = pseudoSweep(interval);
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} else {
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//(c.) otherwise....
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// get random intersections point...
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Collection<Point> tmpIntersections = IntersectionComputer.getInstance().compute(setOfLines, interval.getLower(), interval.getUpper());
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boolean found = false;
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for (Point tmpIntersection : tmpIntersections) {
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if (tmpIntersection.getX() > interval.getLower()
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&& tmpIntersection.getX() < interval.getUpper()) {
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intersectionsPoint = tmpIntersection.getX();
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found = true;
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break;
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}
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}
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if (found) {
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splitActiveSlab(intersectionsPoint, interval);
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//(d.) this may update sigma min
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upperBound(intersectionsPoint);
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//(e.) for i={1,2}, call lower bound(Ui)
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lowerBound(subSlabU1);
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lowerBound(subSlabU2);
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if (subSlabU1.getActivity()) {
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this.intervals.add(subSlabU1);
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}
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if (subSlabU2.getActivity()) {
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this.intervals.add(subSlabU2);
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}
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} else {
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this.intervals.poll();
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}
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}
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} else {
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this.intervals.remove(interval);
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}
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}
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end = System.currentTimeMillis();
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Logging.logInfo("=== E N D - L M S === " + ((end - start) / 1000));
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return pepareResult();
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}
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/**
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* Liefert die Anzahl der Schnittpunkte in einem Intervall
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*
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* @param interval Intervall
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* @return Anzahl der Schnittpunkte
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*/
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public int countInversions(Interval interval) {
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return IntersectionComputer.getInstance().compute(setOfLines, interval.getLower(), interval.getUpper()).size();
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}
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/**
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* In der Literatur wird ein planesweep vorrausgesetzt um in einem Intervall das minimale kMinus Segment zu
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* identifizieren. An dieser Stelle wird eine naivere Lösung verwendet, mithilfe der Schleife werden alle
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* Schnittpunkte betrachtet und bei passenden x-Koordinaten werden wird die vertikale Gerade auf kMinus Segmente
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* untersucht.
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*
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* @param interval
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* @return
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*/
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public Line pseudoSweep(Interval interval) {
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//initialisiere die x-Queue mit den 2D Punkten und sortiere nach x-Lexikographischer Ordnung
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List<Point> xQueue = new ArrayList<>();
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Collection<Point> points = IntersectionComputer.getInstance().compute(setOfLines, interval.getLower(), interval.getUpper());
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for (Point point : points) {
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if (point.getX() >= interval.getLower() && point.getX() < interval.getUpper()) {
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xQueue.add(point);
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}
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}
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Collections.sort(xQueue);
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Line bracelet = sigmaMin;
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double heightOfBracelet = heightsigmaMin;
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for (Point current : xQueue) {
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Double[] currentBracelet = calcKMinusBracelet(current, kMinus);
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if (currentBracelet == null) {
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continue;
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} else if (currentBracelet[0] < heightOfBracelet) {
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heightOfBracelet = currentBracelet[0];
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bracelet = new Line(current.getX(), current.getX(), currentBracelet[1], currentBracelet[2]);
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}
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}
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interval.setActivity(false);
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return bracelet;
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}
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/**
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* Diese Methode spaltet den aktiven Interval an der x Koordinate point. Es werden zwei neue Slabs
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* erzeugt.
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*
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* @param point x Koordinate an der, der Split geschieht.
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*/
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public void splitActiveSlab(double point, Interval active) {
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subSlabU1 = new Interval(active.getLower() + 0.01, point);
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subSlabU2 = new Interval(point, active.getUpper());
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this.intervals.remove(active);
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}
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/**
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* Zu einer vertikalen Gerade werden kMinus Segmente erzeugt und geprüft ob eine bessere Lösung
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* als SigmaMin vorliegt.
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*
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* @param point x-Koordinate zur Konstruktion der vertikalen Gerade
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*/
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public void upperBound(double point) {
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double height = heightsigmaMin;
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double tmpHeight;
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List<Double> sortedLineSequence = getEjValues(point);
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int itnbr = ((n - kMinus) + 1);
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for (int i = 0; i < itnbr; i++) {
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tmpHeight = sortedLineSequence.get((i + kMinus) - 1) - sortedLineSequence.get(i);
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if (tmpHeight < height) {
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height = tmpHeight;
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}
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if (height < heightsigmaMin) {
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heightsigmaMin = height;
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if (sigmaMin != null) {
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sigmaMin.setEndPoints(point, sortedLineSequence.get(i)
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, point, sortedLineSequence.get((i + kMinus) - 1));
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} else {
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sigmaMin = new Line(point, point, sortedLineSequence.get(i),
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sortedLineSequence.get((i + kMinus) - 1));
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}
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}
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}
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}
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/**
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* Die Methode prüft ob das übergebene Intervall die untere Schranke einer potenziellen Lösung erfüllt.
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*
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* @param pslab übergebene Intervall
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*/
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public void lowerBound(Interval pslab) {
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int[] alpha = new int[n];
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int[] beta = new int[n];
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int strictlyGreater = 0;
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//Teil I.
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List<Double> umaxList;
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List<Double> uminList;
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//y koordinaten der Schnittpunkte
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List<Line> lines = new ArrayList<>();
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for (Line p : setOfLines) {
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lines.add(
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new Line(pslab.getLower(), pslab.getUpper(), ((pslab.getLower() * p.getM()) + p.getB()),
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((pslab.getUpper() * p.getM()) + p.getB())));
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}
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umaxList = getEjValues(pslab.getUpper());
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uminList = getEjValues(pslab.getLower());
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for (int i = 0; i < n; i++) {
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Line level = new Line(pslab.getLower(), pslab.getUpper(), uminList.get(i), umaxList.get(i));
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for (Line line : lines) {
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if ((line.getY1() < level.getY1()) && (line.getY2() < level.getY2())) {
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alpha[i]++;
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}
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if ((line.getY1() > level.getY1()) && (line.getY2() > level.getY2())) {
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strictlyGreater++;
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}
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}
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beta[i] = n - (alpha[i] + strictlyGreater);
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strictlyGreater = 0;
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}
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//Teil II.
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int i = 0;
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double h;
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pslab.setActivity(false);
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for (int j = 0; j < n; j++) {
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while ((i < n && (Math.abs(beta[i] - alpha[j]) < kPlus))) {
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i++;
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}
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if (i >= n) {
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pslab.setActivity(false);
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break;
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} else {
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h = Math.min(Math.abs(uminList.get(j) - uminList.get(i)),
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Math.abs(umaxList.get(j) - umaxList.get(i)));
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double error = 0.01;
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if (((1 + error) * h) < heightsigmaMin) {
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pslab.setActivity(true);
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return;
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}
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}
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i = 0;
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}
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}
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/**
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* Berechnet die Schnittpunkte der Geraden und der vertikalen Gerade u. Im paper sind diese Werte
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* als e_j Werte bekannt.
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*
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* @param u vertikale Gerade
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* @return Liste der Schnittpunkte (da u bekannt werden nur die y Werte zurück gegeben)
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*/
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public List<Double> getEjValues(double u) {
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List<Double> ret = new ArrayList<>();
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for (Line p : setOfLines) {
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ret.add((p.getM() * u) + p.getB());
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}
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Collections.sort(ret);
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return ret;
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}
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/**
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* Die Funktion berechnet anhand einer vertikalen Gerade x = px das sogenannte kleinste kMinus
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* Bracelet. Mit anderen Worten es wird eine vertikale Teilgerade berechnet die mindestens kMinus
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* Geraden schneidet und dabei minimal ist.
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*
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* @param px Koordinate um die "vertikale Gerade" zu simulieren.
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* @return Das Array enthält höhe des Bracelet, e_j und e_(j + kMinus - 1)
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*/
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public Double[] calcKMinusBracelet(Point px, int kMinusValue) {
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//y Koordinaten für das kMinus brecalet
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List<Double> intersections = new LinkedList<>();
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for (Line line : setOfLines) {
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intersections.add((px.getX() * line.getM()) + line.getB());
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}
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if (intersections.size() >= kMinusValue) {
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Collections.sort(intersections);
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double height = Math.abs(intersections.get(0) - intersections.get(kMinusValue - 1));
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return new Double[]{height, intersections.get(0), intersections.get(kMinusValue - 1)};
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} else {
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return null;
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}
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}
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private Line pepareResult() {
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if (this.subscriber != null) {
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double m = (getSigmaMin().getX2() + getSigmaMin().getX1()) * 0.5;
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double b = (getSigmaMin().getY2() + getSigmaMin().getY1()) * -0.5;
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slope = m;
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yInterception = b;
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AlgorithmData data = new AlgorithmData();
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data.setType(SubscriberType.LMS);
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data.setLineData(new Line(m, b));
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this.subscriber.onNext(data);
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} else {
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double m = (getSigmaMin().getX2() + getSigmaMin().getX1()) * 0.5;
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double b = (getSigmaMin().getY2() + getSigmaMin().getY1()) * -0.5;
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slope = m;
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yInterception = b;
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}
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return new Line(getSlope(), getYInterception());
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}
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/**
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* @return Anzahl der Geraden
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*/
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public int getN() {
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return n;
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}
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/**
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* @param n Anzahl der Geraden
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*/
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public void setN(int n) {
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this.n = n;
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}
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/**
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* @param quantileError Parameter quantile Fehler
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*/
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public void setQuantileError(double quantileError) {
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this.quantileError = quantileError;
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}
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/**
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* @param kMinus kMinus index
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*/
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public void setkMinus(int kMinus) {
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this.kMinus = kMinus;
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}
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/**
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* @return duale Streifen Sigma_min
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*/
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public Line getSigmaMin() {
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return sigmaMin;
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}
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/**
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* @param sigmaMin duale Streifen Sigma_min
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*/
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public void setSigmaMin(Line sigmaMin) {
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this.sigmaMin = sigmaMin;
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}
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/**
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* @param heightsigmaMin höhe von Sigma_min
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*/
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public void setHeightsigmaMin(double heightsigmaMin) {
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this.heightsigmaMin = heightsigmaMin;
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}
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/**
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* @param constant Parameter Konstante
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*/
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public void setConstant(Double constant) {
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this.constant = constant;
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}
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/**
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* @return Steigung
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*/
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public Double getSlope() {
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return slope;
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}
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/**
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* @return y-Achsenabschnitt
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*/
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public Double getYInterception() {
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return yInterception;
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}
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@Override
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public void subscribe(Flow.Subscriber<? super Data> subscriber) {
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this.subscriber = subscriber;
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}
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}
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